The classical approach to shape from shading problems is to find a numerical
solution of the image irradiance partial differential equation. It is usually
assumed that the parameters of this equation (the light source direction and
surface albedo) can be estimated in advance. For images which contain shadows
and occluding contours, this decoupling of problems is artificial and the
classical approach fails. We develop a new approach to solving these
equations using the image geometric structures instead of the image
photometric structure. Our approach is based on modern differential geometry,
and solves for light source and surface shape changes concurrently. Local
scene elements (scenels) are estimated from the shading flow field and the
tangent field (see Fig. ), and smoothness, material, and
light source compatibility conditions resolve them into consistent scene
descriptions. Shadows and related difficulties for the classical approach are
discussed.

P. Breton, S.W. Zucker

The shading flow field and the tangent field are geometrical structures that characterize respectively, smooth and abrupt changes in image intensity. These geometrical structures were extracted from the image of a sphere illuminated from two distant light sources: the shading flow field is depicted by thin arrows, and the tangent field, by thick arrows.

Mon Nov 13 10:43:02 EST 1995